Unveiling nonlinear heat and convection phenomena in aligned magnetic fields: Insights into variable thermal conductivity and melting heat effects

Nonlinear convection and heat generation in the presence of an aligned magnetic field are numerically analyzed in this work. In a non-Darcy porous material, the two-dimensional flow of a Maxwell fluid over an inclined stretching/shrinking sheet is examined. The study focuses on how heat transport is affected by nonlinear convection, variable thermal conductivity, and melting heat. The governing nonlinear partial differential equations (PDEs) are transformed into nondimensional ordinary differential equations (ODEs) by the use of effective transformations. The built-in bvp4c function in MATLAB is used to obtain numerical solutions. Important results show that with thermal stratification, momentum and thermal profiles behave inversely. Under the same conditions, a significant increase in the skin friction coefficient is noted, and the local Nusselt number rises with increasing values of magnetic constraint, inclined angle, and suction parameter. Furthermore, a greater nonlinear convection parameter results in an improvement in the velocity profile and a decrease in the thermal profile. The findings, which are displayed in tabular and graphical representations, offer important insights into the intricate relationships within the system and may find use in materials engineering, industrial processes, and thermal management.